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We study an elliptic-parabolic free boundary problem in one space dimension. We give several regularity results for both the weak solution and the free boundary. In particular conditions are given which ensure that the free boundary is a C1-curve.doi:10.1090/s0002-9947-1986-0849483-0 fatcat:ajb5jxkh3vgtzn4yqnofq4vgau